16 citations · 26 across the 6 of their papers we have counts for
6 papers
Classification of global and blow-up sign-changing solutions of a semilinear heat equation in the subcritical Fujita range II. Higher-order diffusion
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
Two families of sign-changing solutions of higher-order semilinear parabolic equations are studied.
Variational Approach to Complicated Similarity Solutions of Higher-Order Nonlinear PDEs. II
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce…
Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by ellip…
On convergence in smooth gradient systems with branching of equilibria
V. A. Galaktionov, S. I. Pohozaev, A. E. Shishkov
T.I. Zelenyak's ideas and method of 1968 are shown to apply to N-dimensional second- and higher-order parabolic equtions and ensure a fast exponential convergence to degenerate equ…
On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations
V. A. Galaktionov, E. Mitidieri, S. I. Pohozaev
The initial boundary-value problem (IBVP) and the Cauchy problem for the Kuramoto--Sivashinsky equation and other related th-order semilinear parabolic partial differential equ…
Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves
V. A. Galaktionov, S. I. Pohozaev
Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different te…